# rocsolver_ssytrf_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytrf_batched Interface Reference
hipfort_rocsolver::rocsolver_ssytrf_batched Interface Reference

SYTRF_BATCHED computes the factorization of a batch of symmetric indefinite matrices using Bunch-Kaufman diagonal pivoting. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_ssytrf_batched_ (handle, uplo, n, A, lda, ipiv, strideP, myInfo, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytrf_batched_full_rank (handle, uplo, n, A, lda, ipiv, strideP, myInfo, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytrf_batched_rank_0 (handle, uplo, n, A, lda, ipiv, strideP, myInfo, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_ssytrf_batched_rank_1 (handle, uplo, n, A, lda, ipiv, strideP, myInfo, batch_count)

## Detailed Description

SYTRF_BATCHED computes the factorization of a batch of symmetric indefinite matrices using Bunch-Kaufman diagonal pivoting.

(This is the blocked version of the algorithm).

The factorization has the form

$\begin{array}{cl} A_i = U_i D_i U_i^T & \: \text{or}\newline A_i = L_i D_i L_i^T & \end{array}$

where $$U_i$$ or $$L_i$$ is a product of permutation and unit upper/lower triangular matrices (depending on the value of uplo), and $$D_i$$ is a symmetric block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks $$D_i(k)$$.

Specifically, $$U_i$$ and $$L_i$$ are computed as

$\begin{array}{cl} U_i = P_i(n) U_i(n) \cdots P_i(k) U_i(k) \cdots & \: \text{and}\newline L_i = P_i(1) L_i(1) \cdots P_i(k) L_i(k) \cdots & \end{array}$

where $$k$$ decreases from $$n$$ to 1 (increases from 1 to $$n$$) in steps of 1 or 2, depending on the order of block $$D_i(k)$$, and $$P_i(k)$$ is a permutation matrix defined by $$ipiv_i[k]$$. If we let $$s$$ denote the order of block $$D_i(k)$$, then $$U_i(k)$$ and $$L_i(k)$$ are unit upper/lower triangular matrices defined as

$U_i(k) = \left[ \begin{array}{ccc} I_{k-s} & v & 0 \newline 0 & I_s & 0 \newline 0 & 0 & I_{n-k} \end{array} \right]$

and

$L_i(k) = \left[ \begin{array}{ccc} I_{k-1} & 0 & 0 \newline 0 & I_s & 0 \newline 0 & v & I_{n-k-s+1} \end{array} \right].$

If $$s = 1$$, then $$D_i(k)$$ is stored in $$A_i[k,k]$$ and $$v$$ is stored in the upper/lower part of column $$k$$ of $$A_i$$. If $$s = 2$$ and uplo is upper, then $$D_i(k)$$ is stored in $$A_i[k-1,k-1]$$, $$A_i[k-1,k]$$, and $$A_i[k,k]$$, and $$v$$ is stored in the upper parts of columns $$k-1$$ and $$k$$ of $$A_i$$. If $$s = 2$$ and uplo is lower, then $$D_i(k)$$ is stored in $$A_i[k,k]$$, $$A_i[k+1,k]$$, and $$A_i[k+1,k+1]$$, and $$v$$ is stored in the lower parts of columns $$k$$ and $$k+1$$ of $$A_i$$.

Parameters
 [in] handle rocblas_handle. [in] uplo rocblas_fill. Specifies whether the upper or lower part of the matrices A_i are stored. If uplo indicates lower (or upper), then the upper (or lower) part of A_i is not used. [in] n rocblas_int. n >= 0. The number of rows and columns of all matrices A_i in the batch. [in,out] A array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the symmetric matrices A_i to be factored. On exit, the block diagonal matrices D_i and the multipliers needed to compute U_i or L_i. [in] lda rocblas_int. lda >= n. Specifies the leading dimension of matrices A_i. [out] ipiv pointer to rocblas_int. Array on the GPU of dimension n. The vector of pivot indices. Elements of ipiv are 1-based indices. For 1 <= k <= n, if ipiv_i[k] > 0 then rows and columns k and ipiv_i[k] were interchanged and D_i[k,k] is a 1-by-1 diagonal block. If, instead, ipiv_i[k] = ipiv_i[k-1] < 0 and uplo is upper (or ipiv_i[k] = ipiv_i[k+1] < 0 and uplo is lower), then rows and columns k-1 and -ipiv_i[k] (or rows and columns k+1 and -ipiv_i[k]) were interchanged and D_i[k-1,k-1] to D_i[k,k] (or D_i[k,k] to D_i[k+1,k+1]) is a 2-by-2 diagonal block. [in] strideP rocblas_stride. Stride from the start of one vector ipiv_i to the next one ipiv_(i+1). There is no restriction for the value of strideP. Normal use case is strideP >= n. [out] info pointer to rocblas_int. Array of batch_count integers on the GPU. If info[i] = 0, successful exit for factorization of A_i. If info[i] = j > 0, D_i is singular. D_i[j,j] is the first diagonal zero. [in] batch_count rocblas_int. batch_count >= 0. Number of matrices in the batch.

## ◆ rocsolver_ssytrf_batched_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytrf_batched::rocsolver_ssytrf_batched_ ( type(c_ptr), value handle, integer(kind(rocblas_fill_upper)), value uplo, integer(c_int), value n, type(c_ptr) A, integer(c_int), value lda, type(c_ptr), value ipiv, integer(c_int64_t), value strideP, integer(c_int) myInfo, integer(c_int), value batch_count )

## ◆ rocsolver_ssytrf_batched_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytrf_batched::rocsolver_ssytrf_batched_full_rank ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:,:,:), target A, integer(c_int) lda, integer(c_int), dimension(:), target ipiv, integer(c_int64_t) strideP, integer(c_int) myInfo, integer(c_int) batch_count )

## ◆ rocsolver_ssytrf_batched_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytrf_batched::rocsolver_ssytrf_batched_rank_0 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), target A, integer(c_int) lda, integer(c_int), target ipiv, integer(c_int64_t) strideP, integer(c_int) myInfo, integer(c_int) batch_count )

## ◆ rocsolver_ssytrf_batched_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytrf_batched::rocsolver_ssytrf_batched_rank_1 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:), target A, integer(c_int) lda, integer(c_int), dimension(:), target ipiv, integer(c_int64_t) strideP, integer(c_int) myInfo, integer(c_int) batch_count )

The documentation for this interface was generated from the following file: